On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11
type: Item
instance of: scholarly article
title: On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11
zbMATH Open document ID: 1391.05174
author: Štefko Miklavič
published in: The Electronic Journal of Combinatorics
publication date: 2018-05-25T00:00:00Z
full work available at URL: v25i1p52
review text: Summary: Let \(\Gamma\) denote a bipartite distance-regular graph with diameter \(D\). In [Graphs Comb. 20, No. 1, 47--57 (2004; Zbl 1054.05101)] \textit{J. S. Caughman IV} showed that if \(D \geq 12\), then \(\Gamma\) is \(Q\)-polynomial if and only if one of the following (i)-(iv) holds: (i) \(\Gamma\) is the ordinary \(2D\)-cycle, (ii) \(\Gamma\) is the Hamming cube \(H(D,2)\), (iii) \(\Gamma\) is the antipodal quotient of the Hamming cube \(H(2D,2)\), (iv) the intersection numbers of \(\Gamma\) satisfy \(c_i = (q^i - 1)/(q-1)\), \(b_i = (q^D-q^i)/(q-1)\) \((0 \leq i \leq D)\), where \(q\) is an integer at least \(2\). In this paper we show that the above result is true also for bipartite distance-regular graphs with \(D \in \{9,10,11\}\).
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 6873096
zbMATH Keywords: bipartite distance-regular graphs
zbMATH Keywords: \(Q\)-polynomial property
MaRDI profile type: Publication
cites work: Q3218140
cites work: Q3992965
cites work: Spectra of bipartite \(P\)- and \(Q\)-polynomial association schemes
cites work: The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes
cites work: Bipartite \(Q\)-polynomial quotients of antipodal distance-regular graphs
cites work: The parameters of bipartite \(Q\)-polynomial distance-regular graphs
cites work: Bipartite \(Q\)-polynomial distance-regular graphs
cites work: Almost 2-homogeneous bipartite distance-regular graphs
cites work: Twice Q-polynomial distance-regular graphs are thin
cites work: Distance-regular graphs
cites work: Q3137758
cites work: Bipartite distance-regular graphs: the \(Q\)-polynomial property and pseudo primitive idempotents
cites work: Homogeneous graphs and regular near polygons
cites work: Spin models on bipartite distance-regular graphs
Recommended article: On bipartite \(Q\)-polynomial distance-regular graphs with \(c_{2}=1\)
Recommended article: Bipartite \(Q\)-polynomial distance-regular graphs
Recommended article: On bipartite \(Q\)-polynomial distance-regular graphs with \(c_2 \leqslant 2\)
Recommended article: The parameters of bipartite \(Q\)-polynomial distance-regular graphs
Recommended article: Almost-bipartite distance-regular graphs with the \(Q\)-polynomial property
Recommended article: Dual bipartite Q-polynomial distance-regular graphs
Recommended article: Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets
Recommended article: Bipartite \(Q\)-polynomial quotients of antipodal distance-regular graphs
Recommended article: Bipartite distance-regular graphs: the \(Q\)-polynomial property and pseudo primitive idempotents
Recommended article: A characterization of \(Q\)-polynomial distance-regular graphs
description: scientific article; zbMATH DE number 6873096